Cost function based on the self-organizing map for parameter estimation of chaotic discrete-time systems

摘要

Parameter estimation problem of dynamical systems is an important task in controller design and system identification. In this paper, a novel approach is proposed towards parameter estimation of discrete dynamical systems with chaotic behaviors. Here, we utilize models of attractors to find unknown parameters of a real systems. This method relies on introducing a new cost function based on self-organizing maps (SOM) of measured data obtained from the system. In addition, theoretical justifications and computational complexity analyses are presented regarding the efficiency of SOM-based cost function. Experimental results on several benchmarks showed suitable performances of the proposed cost function compared to previously published cost functions such as Mean-Squared Error (MSE), Return Map Fingerprint (RMF), and Gaussian Mixture Model (GMM).